FANDOM


Brown dwarfs form in molecular clouds due to gravitational collapse, like regular stars. The difference is that their collapse is halted by degeneracy pressure rather than nuclear reactions. Assuming nuclear burning starts at $ T_H \approx 10^{7.5} \, \rm{K} $, the maximum mass for a Brown Dwarf is given by

$ \frac{G M m_p}{R} = k T_H = \frac{h^2}{m_e} \left(\frac{M}{m_p R^3} \right)^{2/3} $

explicitly

[1]$ M \approx \frac{h^{3/2} k^{3/4} T_H^{3/4}}{G^{3/2} m_e^{3/4} m_p^2} \approx 0.04 M_{\odot} $

A more accurate calculates sets the limit at 0.08 solar mass.